Technical Field
This disclosure relates to 3D printing, including compensating for printing errors.
Description of Related Art
Geometric fidelity of 3D printed products can be critical for Additive Manufacturing (AM) to be a direct manufacturing technology. Shape deviations of AM built products can be attributed to multiple variation sources, such as substrate geometry defect, disturbance in process variables, and material phase change.
Three strategies have been reported to improve geometric quality in AM: (1) control process variables x based on the observed disturbance of process variables Δx, (2) control process variables x based on the observed product deviation Δy, and (3) control input product geometry y based on the observed product deviation Δy.
Introduction of 3D Printing
Additive manufacturing (AM) or 3D printing directly fabricates physical products from a 3D CAD model by layered manufacturing processes. Since AM adds material layer by layer to construct products, this technique theoretically enables the direct printing of products with extremely complex geometry. Geometric complexity does not affect building efficiency, and no extra effort is necessary for molding construction or fixture tooling design, making 3D printing one of the most promising manufacturing techniques [Campbell, T., Williams, C., Ivanova, O, and Garrett, B. (2011). Could 3d printing change the world? Technologies, Potential, and Implications of Additive Manufacturing; Gibson, I., Rosen, D., and Stucker, B. (2009). Additive manufacturing technologies: rapid prototyping to direct digital manufacturing. Springer Verlag; Hilton, P. and Jacobs, P. (2000). Rapid tooling: technologies and industrial applications. CRC; Melchels, F., Feijen, J., and Grijpma, D. (2010). A review on stereolithography and its applications in biomedical engineering. Biomaterials, Vol. 31, No. 24, pages 6121-6130].
Despite these promising features, dimensional accuracy control remains a major bottleneck for the application of 3D printing in direct manufacturing. Shape deviations of AM built products can be attributed to multiple variation sources. For instance, [Cohen, D. L. and Lipson, H. (2010). Geometric feedback control of discrete-deposition sff systems, Rapid Prototyping Journal, Vol. 16, No. 5, pages 377-393.] summarized three classes of process uncertainties that could diminish the geometric fidelity of fabricated parts: situational, environmental, and build-material uncertainties with examples of substrate geometry defect, disturbance in process variables, and material phase change in each class, respectively.
TABLE 1Feedback Control Strategies in Additive ManufacturingVariablesVariablesObservedActuatedSample Literature1.Process variables xProcess variables xHu, D., Mei, H., and Kovacevic, R. (2002).substrate orsubstrate orImproving solid freeform fabrication by laser-nozzle positionnozzle positionbased additive manufacturing. Proceedings ofenvelope temperatureenvelope temperaturethe Institution of Mechanical Engineers, Part B:deposition tooldeposition toolJournal of Engineering Manufacture, Vol. 216,temperaturetemperatureNo. 9, pages 1253-1264; Song, L. andlaser powerlaser powerMazumder, J. (2011). Feedback control of meltmaterial feedrate,material feedrate,pool temperature during laser cladding process.etcetcIEEE Transactions on Control SystemsTechnology, Vol. 19, No. 6, pages 1349-1356.2.Product deviationProcess variables xHeralic, A., Christiansson, A.-K., andΔyLennartson, B. (2012). Height control of lasermetal-wire deposition based on iterative learningcontrol and 3d scanning. Optics and Lasers inEngineering, Vol. 50, No. 9, pages 1230-1241;Cohen, D. L. and Lipson, H. (2010). Geometricfeedback control of discrete-deposition sffsystems, Rapid Prototyping Journal, Vol. 16, No.5, pages 377-393.3.Product deviationDesign input ofTong, K., Lehtihet, E., and Joshi, S. (2003).Δyproduct geometry yParametric error modeling and software errorcompensation for rapid prototyping. RapidPrototyping Journal, Vol. 9, No. 5, pages 301-313; Tong, K., Joshi, S., and Lehtihet, E. (2008).Error compensation for fused depositionmodeling (fdm) machine by correcting slice files.Rapid Prototyping Journal, Vol. 14, No. 1, pages4-14; Huang, Q., Zhang, J., Sabbaghi, A., andDasgupta, T. (2014a). Optimal offlinecompensation of shape shrinkage for 3d printingprocesses. IIE Transactions on Quality andReliability, in press; Huang, Q., H., N., Xu, K.,Chen, Y., Sosina, S., and Dasgupta, T. (2014b).Predictive modeling of geometric deviations of3d printed products - a unified modelingapproach for cylindrical and polygon shapes.volume Finalist of Best Application Paper, Taipei,Taiwan, the tenth IEEE International Conferenceon Automation Science and Engineering (CASE2014).
Literature Review on Geometric Quality Control
As summarized in Table 1, three feedback control strategies have been reported to reduce process uncertainties and improve geometric quality in AM: (1) control process variables x based on the observed disturbance of process variables Δx, (2) control process variables x based on the observed product deviation Δy, and (3) control input product geometry y based on the observed product deviation Δy. For instance, in the first category Hu et al. [Hu, D., Mei, H., and Kovacevic, R. (2002). Improving solid freeform fabrication by laser-based additive manufacturing. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, Vol. 216, No. 9, pages 1253-1264.] studied the real-time sensing and control of metal powder delivery in laser-based AM. To achieve a controllable powder delivery, a closed-loop control system based on infrared image sensing was built for control of the heat input and size of the molten pool. Song and Mazumder [Song, L. and Mazumder, J. (2011). Feedback control of melt pool temperature during laser cladding process. IEEE Transactions on Control Systems Technology, Vol. 19, No. 6, pages 1349-1356.] monitored the melt pool temperature of a laser cladding process with a dual-color pyrometer. A state-space dynamic model was establish to relate the laser power with the melt pool temperature. The closed-loop process tracked and stabilized the melt pool temperature to a reference temperature profile.
In the second category, Heralic et al. [Heralic, A., Christiansson, A.-K., and Lennartson, B. (2012). Height control of laser metal-wire deposition based on iterative learning control and 3d scanning. Optics and Lasers in Engineering, Vol. 50, No. 9, pages 1230-1241.], to obtain a flat deposition surface in a Laser Metal-wire Deposition process, controlled the offset of the robot in the vertical direction based on the 3D scanned data. The deviations in the layer height were compensated by controlling the wire feed rate on next deposition layer through iterative learning control. Cohen and Lipson [Cohen, D. L. and Lipson, H. (2010). Geometric feedback control of discrete-deposition sff systems, Rapid Prototyping Journal, Vol. 16, No. 5, pages 377-393.] argued that monitoring the process variables Δx could be limited the extent to which process uncertainties can be detected and corrected. They developed geometric feedback control to directly manipulate the location of deposited matter to compensate for geometric inaccuracies based on the observed whole-part geometry.
In the third category Tong et al. [Tong, K., Lehtihet, E., and Joshi, S. (2003). Parametric error modeling and software error compensation for rapid prototyping. Rapid Prototyping Journal, Vol. 9, No. 5, pages 301-313; Tong, K., Joshi, S., and Lehtihet, E. (2008). Error compensation for fused deposition modeling (fdm) machine by correcting slice files. Rapid Prototyping Journal, Vol. 14, No. 1, pages 4-14.], to control detailed features along the boundary of the printed product, changed the CAD design to compensate for shrinkage, and used polynomial regression models to analyze the shrinkage in X, Y, and Z directions separately. However, prediction of deformation based on the shift of individual points is independent of the geometry of the product, which is not consistent with the physical manufacturing process.
For complete control of all local features around the perimeter of a AM built part, Huang et al. [Huang, Q., Zhang, J., Sabbaghi, A., and Dasgupta, T. (2014a). Optimal offline compensation of shape shrinkage for 3d printing processes. IIE Transactions on Quality and Reliability, in press.] established a generic approach to model and predict part deviations and subsequently derived an optimal compensation plan to achieve dimensional accuracy. The essence of this new modeling approach is to transform in-plane (x-y plane) geometric errors into a functional profile defined on the polar coordinate system. This representation decoupled the geometric shape complexity from the deviation modeling and a generic formulation of shape deviations can thus be achieved. The developed approach was demonstrated both analytically and experimentally in a stereolithography process. Experimental results demonstrate the ability of the proposed compensation approach to achieve an improvement of one order of magnitude in reduction of geometric errors for cylindrical products. However, this study did not demonstrate how the established method can be extended to non-cylindrical products.
Huang et al. [Huang, Q., H., N., Xu, K., Chen, Y., Sosina, S., and Dasgupta, T. (2014b). Predictive modeling of geometric deviations of 3d printed products—a unified modeling approach for cylindrical and polygon shapes. volume Finalist of Best Application Paper, Taipei, Taiwan. the tenth IEEE International Conference on Automation Science and Engineering (CASE 2014).] attempted to connect the model for cylindrical shape with the model for polygon shapes in a unified modeling framework. The proposed model contains a basis function for cylindrical shape and a cookie-cutter basis function to carve out the polygon shape from the cylindrical shape. Experimental and analytical studies of square, pentagon, and dodecagon shapes were conducted to verify the unified model. However, the model fitting results, though good for square and pentagon shapes, need improvement for polygons with large number of sizes. In addition, individual models were fitted for each shape in Huang et al. [Huang, Q., H., N., Xu, K., Chen, Y., Sosina, S., and Dasgupta, T. (2014b). Predictive modeling of geometric deviations of 3d printed products—a unified modeling approach for cylindrical and polygon shapes. volume Finalist of Best Application Paper, Taipei, Taiwan. the tenth IEEE International Conference on Automation Science and Engineering (CASE 2014).], as opposed to a single integrated model. No compensation studies were provided to validate the proposed models.